4. Find the base of a triangle if its height
is 2 3/4 cm and its area is 12 5/8cm². Write
your answer as a mixed number.

We get the translation rule as (x-4, y+5) for triangle ABC.

We are given a triangle:

ABC where

A = (3, -1)

B = (7, -5)

C = (-2, -2)

And, we are also given the translation of the triangle as A'B'C'

where

A' = (-1, 4)

B' = (3, 0)

C' = (-6, 3)

We need to tell the translation rule for it,

For the x coordinate, we can see that:

- 1 - 3 = - 4

3 - 7 = - 4

- 6 - (-2) = -4

So, the rule for x coordinate will be:

x - 4

Now for y coordinate:

4 - (-1) = 5

0 - (-5) = 5

3 - (-2) = 5

So, the rule for y coordinate will be:

y + 5

Translation rule then becomes:

(x-4, y+5)

Therefore, we get the translation rule as (x-4, y+5) for triangle ABC.

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Answer: 4q^2

Step-by-step explanation:

(-2q)^2=

(-2*q)^2=

(-2)^2 * q^2=

4 * q^2=4q^2

The following are the linear relationships between two variables measured in statistics:

So,

The following are the linear relationships between two variables measured in statistics:

Therefore, the following are the linear relationships between two variables measured in statistics:

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The volume of the given square pyramid in cubic feet is 2.5 cubic feet.

Given that, a square pyramid has a volume of 4320 cubic inches.

We need to find the volume of this pyramid in cubic feet.

The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height).

To convert from cubic inches to cubic feet, divide your cubic inches figure by 1728.

Now,  4320/1728 = 2.5 cubic feet

Therefore, the volume of the given square pyramid in cubic feet is 2.5 cubic feet.

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Answer:

q = 20

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

180 - 78 = 102

so

5q+2 = 102

subtract 2 from both sides

5q = 100

100 / 5 = 20

5q / 5 = q

q = 20

Hope this makes sense.

The students she's had in 7 years is 850.

It should be noted that we want to find the 7th term. This will be:

a + (n - 1)d

a = First term = 250

d = Difference = 100

n = Number = 7

Therefore, a + (n - 1)d

= 250 + (7 - 1)100

= 250 + 600

= 850

Therefore, the students she's had in 7 years is 850.

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60-100 bpm and that is the range of a 16 year old heart beat

Answer:

Step-by-step explanation:

Lower limit of range:

H = [tex]\frac{7}{10}[/tex](220-a)

a = 16 [given]

∴ H = [tex]\frac{7}{10}[/tex](220-16)

H = [tex]\frac{7}{10}[/tex](204)

H = [tex]\frac{7}{10}[/tex]×[tex]\frac{204}{1}[/tex]

H = [tex]\frac{1428}{10}[/tex]

H = 142.8

H = 143 beats per minute [as an integer]

Answer: 13 ==> B

Step-by-step explanation:

x=-3, y=4, z=-1

|2x-3y|+5z=

|2(-3)-3(4)|+5(-1)=

|-6-12|-5=

|-18|-5=

18-5=13 ==> B

Answer:

-6<x<0

Step-by-step explanation:

-8|x/3+1|>-8

-8|x/3+1|/(-8)>-8/(-8)

|x/3+1|<1

x/3+1<1

x/3<0

x<0

x/3+1>-1

x/3>-2

x>-6

-6<x<0

Answer:

Y= (-27)

Step-by-step explanation:

Well, I am assuming your just looking for Y. So what I did was you'd want to get rid of the fraction first. I multiplied 3 to all the numbers. so -12(3) = 6(3) + 2y since the bottom 3 from the fraction cancelled out with the (3). so now it would be -36=18+2y. -54/2=2y/2 which leads to -27. So I think Y= -27.

Changing the class width from 4,000 to 3,000 increases the details of the frequency distribution, thereby providing a better summary of the data.

Based on a similar question, the possible part of the question appear left out includes.

The correct response is; Yes, the value or magnitude categories of the data are increased using the smaller class width of 3,000 such that more details about the influence of the different classes on the results are seen, which provides a better summary of the information in the data than the frequency distribution that a 4,000 class width.

The overall shape of the frequency histogram remains almost the same for both class widths

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Answer: X= -8

Step-by-step explanation:

Rearrange your terms:

5-X=13

-x+5+13

Subtract 5 from both sides

Simplify those = -X = 8

Dive both sides by same factor, -1

Simplify again

Solution= X= -8

The weight of each bag is 23.25 pounds.

For given question,

Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags.

If all the bags were identical, we need to find the weight of each bag.

Let 'm' be the weight of each bag.

As Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags and all the bags were identical, we get an expression.

8 × m = 187.6

now we solve above expression to find the value of m i.e., to find the weight of each bag.

⇒ 8 × m = 187.6

⇒ m = 187.6 / 8

⇒ m = 23.25 pounds

Therefore, the weight of each bag is 23.25 pounds.

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Answer:

Step-by-step explanation:

from the sign it's a right angle, so 90°

90 = x - 8 + 6x

90 + 8 = 7x

98 = 7x

x = 98 : 7

x = 14

------------------

check

90 = 14 - 8 + 6 * 14       (remember pemdas)

90 = 14 - 8 + 84

90 = 90

the answer is good

Find angle 1

x - 8

14 - 8 =

6°

Find angle 2

6x

6 * 14 = 84°

--------------------

check

84 + 6 = 90°

the answer is good

Answer:

[tex]\textsf{a)} \quad \textsf{Equation}: \quad \boxed{x-8+6x=90}[/tex]

[tex]\begin{aligned}\textsf{b)} \quad m \angle 1 & =\boxed{6^{\circ}}\\ m \angle 2 & =\boxed{84^{\circ}}\end{aligned}[/tex]

Step-by-step explanation:

From inspection of the given diagram, the sum of the two angles is 90° (indicated by the right angle sign):

[tex]\implies m \angle 1+m \angle 2=90^{\circ}[/tex]

[tex]\implies (x - 8)^{\circ} + (6x)^{\circ} = 90^{\circ}[/tex]

[tex]\implies x-8+6x=90[/tex]

[tex]\textsf{Equation}: \quad \boxed{x-8+6x=90}[/tex]

To find the measure of each angle, solve the equation for x:

[tex]\implies x-8+6x=90[/tex]

[tex]\implies x+6x-8=90[/tex]

[tex]\implies 7x-8=90[/tex]

[tex]\implies 7x-8+8=90+8[/tex]

[tex]\implies 7x=98[/tex]

[tex]\implies \dfrac{7x}{7}=\dfrac{98}{7}[/tex]

[tex]\implies x=14[/tex]

Substitute the found value of x into the expression for each angle:

[tex]\implies m \angle 1=(x-8)^{\circ}[/tex]

[tex]\implies m \angle 1=(14-8)^{\circ}[/tex]

[tex]\implies m \angle 1=\boxed{6^{\circ}}[/tex]

[tex]\implies m \angle 2=(6x)^{\circ}[/tex]

[tex]\implies m \angle 2=(6 \cdot 14)^{\circ}[/tex]

[tex]\implies m \angle 2=\boxed{84^{\circ}}[/tex]

Answer:

10

Step-by-step explanation:

|-2(2) + (-3)(2)|

2(2) + 3(2)

4 + 6

| | indicate absolute value, negative numbers are turned to positive numbers in absolute value, making B and C (negative values) into positive values.

The sum of the first 13 terms is 260

The first term(a) is 2

The common difference(d) is 3

n= 13

The formular is

n/2(2a + (n-1)d)

= 13/2 [ 2(2) + (13-1)3]

= 6.5 [4 + 12(3)]

= 6.5 [4 + 36]

= 6.5(40)

= 260

Hence the sum of the first 13 terms is 260

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Answer: The length of AB =4 units

               The length of BD = 2.4 units.

Step-by-step explanation:

Given data,

                  AD = 3.2 unit

                  BC  = 3 unit

                 CD  = 1.8 units

Find :         AB =? units

                  BD=? units

We can use the formula of Pythagorean theorem,

Define Pythagorean theorem :

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

Hypotenuse2 = Perpendicular2 + Base2

                  c2 = a2 + b2

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

Let be a ΔABC,

                           [tex](AB)^{2} = (BC)^{2} +(AC)^{2}[/tex]

From the above formula now  determined  the value of AB and BD,

Firstly , find the value of BD

In ΔBDC, by applying Pythagorean theorem,

                             [tex](BC)^{2} = (BD)^{2} + (DC)^{2}[/tex]             (Eq - 1)

Substitute BC and CD values in equation 1,

            BC  = 3 units and CD = 1.8 units

So,

We can write,

                            [tex]3^{2} = (BD)^{2} +(1.8)^{2}[/tex]

                            9 = [tex](BD)^{2}[/tex] + 3.24

                            [tex](BD)^{2}[/tex] = 9 - 3.24

                            [tex](BD)^{2}[/tex] = 5.76

                             [tex]BD = \sqrt{5.76}[/tex]

                             BD = 2.4 units             (Eq - 2)

Now find the value of AB,

In ΔABD, by applying Pythagorean theorem,

                               [tex](AB)^{2} = (AD)^{2} +(BD)^{2}[/tex]           (Eq - 3)

Substitute AD and BD values in equation 3,

            AD  = 3.2 units and BD = 3 units

So,

We can write,

                                [tex](AB)^{2} = (3.2)^{2} + 3^{2}[/tex]

                                 [tex](AB)^{2}[/tex] = 10.24 + 5.76

                                 [tex](AB)^{2}[/tex] = 16

                                  AB = [tex]\sqrt{16}[/tex]

                                   AB = 4 units

Therefore,

The length of AB =4 units

The length of BD = 2.4 units.

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(a) The mean of (2) will be greater than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the maximum of (1) is smaller than the maximum of (2)

(b) The mean of (2) will be smaller than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the minimum of (2) is smaller but negative than the minimum of (1) which is also negative.

(c) The mean of (2) will be more than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the maximum of (1) is smaller than the maximum of (2)

(d) The mean of (2) will be smaller than the mean of (1) and the distribution of (2) will have smaller variation as compared to the distribution of (1) because the range of (1) is greater than the range of (2)

The mean is a measure of the central trend of a probability distribution along the median and the mode.

a distribution is the set of all possible values for terms representing defined events.

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The money you will have invested at one year is $560

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are:

Initial = $200

Rate = $30

Let the number of months be n

So, we have

f(n) = Initial + Rate * n

This gives

f(n) = 200 + 30n

There are 12 months in a year

So, we have:

f(12) = 200 + 30 * 12

Evaluate

f(12) = 560

Hence, the money you will have invested at one year is $560

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Explanation:

To add a negative number, we are basically subtracting it because of this:
Example:
10 - 5 = 5

10 + (-5) = 5

The negative sign cancels out the positive which makes it into a subtraction problem instead.

Answer:

132

Step-by-step explanation:

Answer:

3800

Step-by-step explanation:

(52-2)×(8×10-4)

50(80-4)

50×76=3800

Solution in Scientific Notation:

[tex]3.8[/tex] × [tex]10^{3}[/tex]

Hope this helps!

Considering the images (a),(b),(c),(d),(e),(f) the oriented path is

(a) Negative

(b) Positive

(c) Positive

(d) Zero

(e) Zero

(f) Zero

calculating each quadrant's line integral and symmetry.

In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.

What does a Line integral mean?

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Answer:

$8.95

Step-by-step explanation:

Divide 107.4 by 12 and you end up with the price of each audio book.

The same can be said for each problem you want find the individual amount of

Answer:

Each audio book costs $8.95

Step-by-step explanation:

Since 12 audio books that are at all the same prize equal $107.4, therefore in order to find the total of each book we divide $107.4 by 12

➟ 107.4 ÷ 12

➟ 8.95

∴ $8.95 is the cost of each book

Answer:

According to my the answer is 32

Step-by-step explanation:

cuz 4 ÷ 1/8 becomes 4×8/1

which is 32

Answer: 89633.78

Step-by-step explanation: Hope this helps :)

Answer:

True

(If it has 4 sides it is also known as a Quadrilateral!)

Step-by-step explanation:

Answer:

yes

the reson for htis is b/c retangles are qudrilateral and quadtrialterals have four sides

The equivalent expression using laws of exponents gives us; 2 over quantity 9 times d raised to the negative fourteenth power end quantity

We want to write an equivalent expression for 4 times d raised to the negative fifth power all over quantity 18 times d raised to the ninth power end quantity. This can be expressed as;

4d⁻⁵/18d⁹

Now, according to laws of exponents, we know that;

x²/x³ = x²⁻³ = x⁻¹

Applying that law to our question gives us;

4d⁻⁵/18d⁹ = (4/18)(d⁻⁵⁻⁹)

= (4/18)(d⁻¹⁴)

Now, the expression 4/18 can be broken down to 2/9. Thus, our final expression is; ²/₉d⁻¹⁴

Writing that in words gives;

2 over quantity 9 times d raised to the negative fourteenth power end quantity

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Answer: 2/9d^14 or 2 over 9 times d to the 14th power

Step-by-step explanation: AFOKE88 gave the same answer. this answer is correct you just have to understand how to write this equation in word form to understand them. they also gave a great explanation for those who need it.

The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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Answer:

185

Step-by-step explanation:

Answer:

185

Factor:

5×37